Вычисли значение выражения 1. $\frac{a^9 \cdot a^{12}}{a^{18}}$ при а=4

Конечно, сейчас помогу! **Задание 10** 1. $\frac{a^9 \cdot a^{12}}{a^{18}} = \frac{a^{9+12}}{a^{18}} = \frac{a^{21}}{a^{18}} = a^{21-18} = a^3 = 4^3 = 64$ 2. $\frac{a^{12} \cdot a^6}{a^{14}} = \frac{a^{12+6}}{a^{14}} = \frac{a^{18}}{a^{14}} = a^{18-14} = a^4 = 3^4 = 81$ 3. $\frac{a^{11} \cdot a^9}{a^{18}} = \frac{a^{11+9}}{a^{18}} = \frac{a^{20}}{a^{18}} = a^{20-18} = a^2 = 7^2 = 49$ 4. $\frac{a^9 \cdot a^8}{a^{12}} = \frac{a^{9+8}}{a^{12}} = \frac{a^{17}}{a^{12}} = a^{17-12} = a^5 = 2^5 = 32$ 5. $\frac{a^{16} \cdot a^{-7}}{a^8} = \frac{a^{16+(-7)}}{a^8} = \frac{a^9}{a^8} = a^{9-8} = a^1 = a = 3$ 6. $\frac{a^{18} \cdot a^{-6}}{a^{10}} = \frac{a^{18+(-6)}}{a^{10}} = \frac{a^{12}}{a^{10}} = a^{12-10} = a^2 = 5^2 = 25$ 7. $\frac{a^{17} \cdot a^{-6}}{a^9} = \frac{a^{17+(-6)}}{a^9} = \frac{a^{11}}{a^9} = a^{11-9} = a^2 = 4^2 = 16$ 8. $\frac{a^{19} \cdot a^{-11}}{a^5} = \frac{a^{19+(-11)}}{a^5} = \frac{a^8}{a^5} = a^{8-5} = a^3 = 5^3 = 125$ 9. $\frac{(a^4)^5}{a^{18}} = \frac{a^{4 \cdot 5}}{a^{18}} = \frac{a^{20}}{a^{18}} = a^{20-18} = a^2 = 6^2 = 36$ 10. $\frac{(a^8)^2}{a^{11}} = \frac{a^{8 \cdot 2}}{a^{11}} = \frac{a^{16}}{a^{11}} = a^{16-11} = a^5 = 2^5 = 32$ 11. $\frac{(a^2)^2}{a^{13}} = \frac{a^{2 \cdot 2}}{a^{13}} = \frac{a^4}{a^{13}} = a^{4-13} = a^{-9} = 5^{-9} = \frac{1}{5^9} = \frac{1}{1953125}$ 12. $\frac{(a^3)^5}{a^{11}} = \frac{a^{3 \cdot 5}}{a^{11}} = \frac{a^{15}}{a^{11}} = a^{15-11} = a^4 = 3^4 = 81$ **Задание 11** 1. $a^6 \cdot a^{18} : a^{20} = a^{6+18} : a^{20} = a^{24} : a^{20} = a^{24-20} = a^4 = 2^4 = 16$ 2. $a^{13} \cdot a^{11} : a^{21} = a^{13+11} : a^{21} = a^{24} : a^{21} = a^{24-21} = a^3 = 4^3 = 64$ 3. $a^7 \cdot a^{10} : a^{14} = a^{7+10} : a^{14} = a^{17} : a^{14} = a^{17-14} = a^3 = 5^3 = 125$ 4. $a^9 \cdot a^{12} : a^{17} = a^{9+12} : a^{17} = a^{21} : a^{17} = a^{21-17} = a^4 = 3^4 = 81$ 5. $a^{21} \cdot a^{-8} : a^{11} = a^{21+(-8)} : a^{11} = a^{13} : a^{11} = a^{13-11} = a^2 = 5^2 = 25$ 6. $a^{27} \cdot a^{-15} : a^9 = a^{27+(-15)} : a^9 = a^{12} : a^9 = a^{12-9} = a^3 = 3^3 = 27$ 7. $a^{25} \cdot a^{-4} : a^{16} = a^{25+(-4)} : a^{16} = a^{21} : a^{16} = a^{21-16} = a^5 = 2^5 = 32$ 8. $a^{19} \cdot a^{-8} : a^9 = a^{19+(-8)} : a^9 = a^{11} : a^9 = a^{11-9} = a^2 = 6^2 = 36$ **Задание 12** 1. $a^{-14} \cdot (a^9)^2 = a^{-14} \cdot a^{9 \cdot 2} = a^{-14} \cdot a^{18} = a^{-14+18} = a^4 = 3^4 = 81$ 2. $a^{-12} \cdot (a^7)^2 = a^{-12} \cdot a^{7 \cdot 2} = a^{-12} \cdot a^{14} = a^{-12+14} = a^2 = 6^2 = 36$ 3. $a^{-12} \cdot (a^5)^3 = a^{-12} \cdot a^{5 \cdot 3} = a^{-12} \cdot a^{15} = a^{-12+15} = a^3 = 4^3 = 64$ 4. $a^{-15} \cdot (a^5)^4 = a^{-15} \cdot a^{5 \cdot 4} = a^{-15} \cdot a^{20} = a^{-15+20} = a^5 = 2^5 = 32$ 5. $a^{-9} \cdot (a^2)^6 = a^{-9} \cdot a^{2 \cdot 6} = a^{-9} \cdot a^{12} = a^{-9+12} = a^3 = 5^3 = 125$ 6. $a^{-8} \cdot (a^5)^2 = a^{-8} \cdot a^{5 \cdot 2} = a^{-8} \cdot a^{10} = a^{-8+10} = a^2 = 3^2 = 9$ 7. $a^{-13} \cdot (a^8)^2 = a^{-13} \cdot a^{8 \cdot 2} = a^{-13} \cdot a^{16} = a^{-13+16} = a^3 = 2^3 = 8$ 8. $a^{-10} \cdot (a^4)^3 = a^{-10} \cdot a^{4 \cdot 3} = a^{-10} \cdot a^{12} = a^{-10+12} = a^2 = 4^2 = 16$ 9. $(a^3)^{-4} : a^{-14} = a^{3 \cdot (-4)} : a^{-14} = a^{-12} : a^{-14} = a^{-12 - (-14)} = a^{-12+14} = a^2 = 5^2 = 25$ 10. $(a^2)^{-6} : a^{-15} = a^{2 \cdot (-6)} : a^{-15} = a^{-12} : a^{-15} = a^{-12 - (-15)} = a^{-12+15} = a^3 = 4^3 = 64$ 11. $(a^4)^{-3} : a^{-17} = a^{4 \cdot (-3)} : a^{-17} = a^{-12} : a^{-17} = a^{-12 - (-17)} = a^{-12+17} = a^5 = 2^5 = 32$ 12. $(a^5)^{-3} : a^{-19} = a^{5 \cdot (-3)} : a^{-19} = a^{-15} : a^{-19} = a^{-15 - (-19)} = a^{-15+19} = a^4 = 3^4 = 81$ 13. $(a^2)^{-8} : a^{-18} = a^{2 \cdot (-8)} : a^{-18} = a^{-16} : a^{-18} = a^{-16 - (-18)} = a^{-16+18} = a^2 = 7^2 = 49$ 14. $(a^4)^{-4} : a^{-19} = a^{4 \cdot (-4)} : a^{-19} = a^{-16} : a^{-19} = a^{-16 - (-19)} = a^{-16+19} = a^3 = 5^3 = 125$ 15. $(a^7)^{-2} : a^{-16} = a^{7 \cdot (-2)} : a^{-16} = a^{-14} : a^{-16} = a^{-14 - (-16)} = a^{-14+16} = a^2 = 3^2 = 9$ 16. $(a^3)^{-5} : a^{-18} = a^{3 \cdot (-5)} : a^{-18} = a^{-15} : a^{-18} = a^{-15 - (-18)} = a^{-15+18} = a^3 = 2^3 = 8